Challenges....
If the solutions to any challenges are not here, send me an email and ask to have them posted here.
• Quant Quiz: Plot of Logarithm and Exponential: The only unusual part here is that the log function is downward sloping instead of upward sloping (as it would be for base b larger than 1).
• Quant Quiz: Long-Short III: If you are underweight a stock but not short and the market moves against you, the size of your active bet increases.
• Quant Quiz: Correlation I: Deeper Challenge: They are almost perfectly negatively correlated because the five-day return to Stock 1 is, essentially, the mean times five plus X, where X is a random variable, and the five-day return to Stock 2 is, essentially, the mean times five minus X, where X is the same random variable.
• Simple pmf with \beta_1=0, but it is non-symmetrical: X={-3,-2,-1,0,1,2,3} with frequencies {1,0,18,72,13,4,0}, taken from an example here. Note that you only need to have \mu_3=0 (assuming some dispersion), to get \beta_1=0.
• Figure 2.15 Exercise: I calculated betas relative to the portfolio with return 0.15.
• Figure 2.17 Exercise: The value of lambda_R is 0.07 (or 7 if expressed in decimals).
• The BEAR challenge. You should get BEAR--->EAR because eventually the balance grows so large that the extra \$1000 arriving each year is nothing.
• The two P/E challenges are straightforward enough.

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